New formulation of Hardin-Pope equations for aeroacoustics

J.A. Ekaterinaris

    Research output: Contribution to journalJournal articleResearch

    Abstract

    Predictions of aeroacoustic disturbances generated by low-speed unsteady flows can be obtained with the two-step method proposed by Hardin and Pope (Hardin, J. C., and Pope, S. D., "An Acoustic/Viscous Splitting Technique for Computational Aeroacoustics," Theoretical and Computational Fluid Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented. The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic flowfield generated by a corotating vortex pair. Computed results are compared with the analytic solution.
    Original languageEnglish
    JournalA I A A Journal
    Volume37
    Issue number9
    Pages (from-to)1033-1039
    ISSN0001-1452
    DOIs
    Publication statusPublished - 1999

    Cite this

    Ekaterinaris, J.A. / New formulation of Hardin-Pope equations for aeroacoustics. In: A I A A Journal. 1999 ; Vol. 37, No. 9. pp. 1033-1039.
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    title = "New formulation of Hardin-Pope equations for aeroacoustics",
    abstract = "Predictions of aeroacoustic disturbances generated by low-speed unsteady flows can be obtained with the two-step method proposed by Hardin and Pope (Hardin, J. C., and Pope, S. D., {"}An Acoustic/Viscous Splitting Technique for Computational Aeroacoustics,{"} Theoretical and Computational Fluid Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented. The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic flowfield generated by a corotating vortex pair. Computed results are compared with the analytic solution.",
    keywords = "Vindenergi og atmosf{\ae}riske processer",
    author = "J.A. Ekaterinaris",
    year = "1999",
    doi = "10.2514/2.829",
    language = "English",
    volume = "37",
    pages = "1033--1039",
    journal = "A I A A Journal",
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    publisher = "American Institute of Aeronautics and Astronautics, Inc.",
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    New formulation of Hardin-Pope equations for aeroacoustics. / Ekaterinaris, J.A.

    In: A I A A Journal, Vol. 37, No. 9, 1999, p. 1033-1039.

    Research output: Contribution to journalJournal articleResearch

    TY - JOUR

    T1 - New formulation of Hardin-Pope equations for aeroacoustics

    AU - Ekaterinaris, J.A.

    PY - 1999

    Y1 - 1999

    N2 - Predictions of aeroacoustic disturbances generated by low-speed unsteady flows can be obtained with the two-step method proposed by Hardin and Pope (Hardin, J. C., and Pope, S. D., "An Acoustic/Viscous Splitting Technique for Computational Aeroacoustics," Theoretical and Computational Fluid Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented. The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic flowfield generated by a corotating vortex pair. Computed results are compared with the analytic solution.

    AB - Predictions of aeroacoustic disturbances generated by low-speed unsteady flows can be obtained with the two-step method proposed by Hardin and Pope (Hardin, J. C., and Pope, S. D., "An Acoustic/Viscous Splitting Technique for Computational Aeroacoustics," Theoretical and Computational Fluid Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented. The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic flowfield generated by a corotating vortex pair. Computed results are compared with the analytic solution.

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